$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 3x + 4$ and $ JT = 6x - 8$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x + 4} = {6x - 8}$ Solve for $x$ $ -3x = -12$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({4}) + 4$ $ JT = 6({4}) - 8$ $ CJ = 12 + 4$ $ JT = 24 - 8$ $ CJ = 16$ $ JT = 16$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {16} + {16}$ $ CT = 32$